Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject by first developing the theory of Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates. The authors then introduce semi-Markov chains and hidden semi-Markov chains, before developing related estimation and filtering results. Genomics applications are modelled by discrete observations of these hidden semi-Markov chains. This book contains new results and previously unpublished material not available elsewhere. The approach is rigorous and focused on applications Read more...
Abstract:
Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject, developing the theory of Markov and semi-Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates. Read more...
Author(s): Elliott, Robert J.; Van der Hoek, John
Series: London Mathematical Society lecture note series 445
Publisher: Cambridge University Press
Year: 2018
Language: English
Pages: 174
Tags: Hidden Markov models.;Stochastic processes.;Markov processes.;Hidden Markov models;Markov processes;Stochastic processes
Content: Preface
1. Observed Markov chains
2. Estimation of an observed Markov chain
3. Hidden Markov models
4. Filters and smoothers
5. The Viterbi algorithm
6. The EM algorithm
7. A new Markov chain model
8. Semi-Markov models
9. Hidden semi-Markov models
10. Filters for hidden semi-Markov models
Appendix A. Higher order chains
Appendix B. An example of a second order chain
Appendix C. A conditional Bayes theorem
Appendix D. On conditional expectations
Appendix E. Some molecular biology
Appendix F. Earlier applications of hidden Markov chain models
References
Index.
